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<p>Akira Saito conjectured that every 3-connected line graph of diameter at most 3 is hamiltonian unless it is the line graph of a graph obtained from the Petersen graph by adding at least one pendant edge to each vertex, see [Graphs Combin. 18 (2002) 565-571]. In this paper, we show that a 3-connected claw-free graph of diameter at most 3 has a 2-factor with at most two components. This extends the main result of Kriesell [Graphs Combin. 18 (2002) 565-571].</p>

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Every 3-Connected Claw-Free Graph of Diameter at Most 3 has a 2-Factor with at Most Two Components

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Lei Zhang,
  • Liming Xiong

摘要

Akira Saito conjectured that every 3-connected line graph of diameter at most 3 is hamiltonian unless it is the line graph of a graph obtained from the Petersen graph by adding at least one pendant edge to each vertex, see [Graphs Combin. 18 (2002) 565-571]. In this paper, we show that a 3-connected claw-free graph of diameter at most 3 has a 2-factor with at most two components. This extends the main result of Kriesell [Graphs Combin. 18 (2002) 565-571].